Question

Given: ABCD is a parallelogram; <1 is congruent to <2

To Prove: ABCD is a Rhombus

Plan: Show <2 is congruent to < CAB.
hence CB is congruent to AB,
making ABCD a parallelogram
with consecutive sides congruent


PROOF

Statements Reasons
1. ABCD is a parallelogram 1.Given
<1 is congruent to <2
2. Draw segment from A to C 2. Two points determine exactly one line
3.< 1 & <3 are congruent 3. Alternate angles are congruent
4. AC bisects angle 1&2 4. Def. of Angle bisector
5 . m<DAB=m<BCD 5. Opposite angles in a parallelogram are equal
6. <2 & <3 are congruent 6. Transitive prop 7 . AB=BC 7. Sides oposite are congruent angles
8.<1 & <2 8. Cor.parts are eual
9. AB=BC=CD=DA 9. ABCD is a rhombus

Answer 1

Given that ABCD is a parallelogram with , mABC = 5x + 40, and mBCD = ax, find the value of a.

Answer 2

given rhombus ABCD, with diagonal BD and m<ABD=40,what is the m<A?

Answer 3

a=2/5
b= 2/3
d= 6/5